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ganeshie8

  • one year ago

Just want to share this neat idea for why \(-\times-=+\)

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  1. karatechopper
    • one year ago
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    oh oh oh go I'm listening! :D

  2. anonymous
    • one year ago
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    spit that fire

  3. ganeshie8
    • one year ago
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    let \(r_1\) and \(r_2\) be two positive numbers, then : \[\large (-r_1)(-r_2) = (r_1e^{i\pi})(r_2e^{i\pi})=r_1r_2e^{i2\pi}=r_1r_2\]

  4. anonymous
    • one year ago
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    neat idea, thanks

  5. ikram002p
    • one year ago
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    that wouls also explain why -×+=- i loved it

  6. ganeshie8
    • one year ago
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    didn't want to add anything as it looks so elegant+complete as an one liner xD But here some explanation : To multiply two complex numbers, we simply "multiply the two lengths" to get the resulting length and "add the two angles" to get the resulting angle. \[(r_1,\theta_1)*(r_2,\theta_2)=(r_1r_2,~\theta_1+\theta_2)\] Next notice that the angle for any negative number is \(\pi\) as they fall on the negative real axis. Consequently, multiplying two negative numbers adds up the angles\((\pi+\pi)\) taking the result to positive real axis.

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